The Chancellor has told Mrs May directly that he will not stand down after Cabinet colleagues accused him of “undermining Brexit”.

He will today defend his role as Chancellor in warning of the potential risks of Brexit during an appearance before MPs on the Treasury select committee.

An ally of Mr Hammond told The Daily Telegraph he has made it “absolutely clear” to Mrs May that he will not stand down as Chancellor.

The source said that he believes he is the “right man for difficult times” and won’t be “pushed about” by Brexit ministers.

Theresa May’s key quotes on BrexitPlay!01:56

He will not formally rule out any options for post-Brexit Britain until after elections in Germany and France next year, the source said.

“Sanity will prevail when economic interests assert themselves more strongly than the political ones after the elections in Europe,” the source said.

“The Brexiteers can say what they like but the economic realities are what they are. He has made it absolutely clear to Theresa that he is here to stay. His responsibility will be to keep the econiomy in the best shape possible.

“He is a man who is guided by the figures and the facts. Where there are risks he will not be afraid to spell them out.”

There are very big personalities arguing different things. It’s not easy

It came as Theresa May made clear that she will introduce a “targeted visa system” to cut the number of EU migrants coming to the UK.

She has ordered the Government’s immigration task force, which she personally chairs, to draw up measures to help reduce net migration to less than 100,000 a year after Brexit.

The terms of reference yesterday disclosed that the task force will “ensure an efficient and targeted visa system” and “make it harder for illegal immigrants to stay in the country”.

It is understood that Mr Hammond was one of a number of voices urging caution during a Brexit Cabinet meeting last week, when proposals were discussed for a new work permit system were discussed.

Amber Rudd, the Home Secretary, presented plans for a post-Brexit visa regime that would see all EU workers forced to prove they have secured a skilled job before being allowed into Britain.

Sources claimed that Mr Hammond raised questions about the plans, and that there are fears that the Chancellor could resign over the tensions.

It yesterday emerged that Mr Hammond’s more cautious approach has the support of several Cabinet ministers including Greg Clark, the Business Secretary, and Damian Green the Work and Pensions Secretary.

The Cabinet splits over Britain’s future after it leaves the EU prompted the Prime Minister’s Official Spokeswoman to express her “full confidence” in Mr Hammond.